This document discusses the key mathematical processes that students use to learn and apply mathematics. It defines mathematical processes as the methods through which students acquire and apply mathematical knowledge, concepts, and skills. The key processes discussed are problem solving, reasoning and proving, reflecting, connecting, communicating, representing, and selecting tools and strategies. Each process is defined and examples of how students can develop skills in each process are provided.

1. KLE Society’s College of Education
P.G Department of
Education,Vidyanagar.Hubballi-31
Seminar Topic: mathematical processes
Subject: UDP- Mathematics
Submitted By: Pavan Shrinivas Naik
Submitted To : Shri Veeresh A Kalakeri

2. KLE Society’s College of Education
P.G Department of
Education,Vidyanagar.Hubballi-31
CERTIFICATE
This is to certify that Shri Pavan Shrinivas Naik has satisfactory
completed the seminar in Mathematical processes prescribed
by the Karnataka University, Dharwad for the B.Ed degree
course during 2021-2022
Date:
Signature of teacher in charge of course

3. Mathematical Processes
Introduction
• Students learn and apply the mathematical
processes as they work to achieve the
expectations outlined in the curriculum. All
students are actively engaged in applying these
processes throughout the program.
• They apply these processes, together with social-
emotional learning (SEL) skills, across the
curriculum to support learning in mathematics.

4. Mathematical Processes
Meaning of Mathematical process
• The mathematical processes can be seen
as the processes through which all students
acquire and apply mathematical knowledge,
concepts, and skills. These processes are
interconnected. Problem solving and
communicating have strong links to all the
other processes.

5. Mathematical Processes
Definition of Mathematical process
• (mathematics) calculation by mathematical
methods
• “the problems at the end of the chapter
demonstrated the mathematical
processes involved in the derivation”

6. Mathematical Processes
Example of Mathematical process
• Find the first derivative of f( )
• Find the area of the region that is bounded by
(x =1), (x= 4), (y= 0),
• After justifying its applicability, verify the
conclusions of the Mean-Value Theorem for
the function f ( )over the interval [0
2].

7. The mathematical processes that support effective
learning in mathematics are as follows:
• problem solving
• reasoning and proving
• reflecting
• connecting
• communicating
• representing
• selecting tools and strategies

8. Problem solving
• It is central to doing mathematics. By learning to solve
problems and by learning through problem solving,
students are given, and create, numerous opportunities to
connect mathematical ideas and to develop conceptual
understanding.
• Problem solving forms the basis of effective mathematics
programs that place all students’ experiences and queries
at the centre. Thus, problem solving should be the mainstay
of mathematical instruction.
• It is considered an essential process through which all
students are able to achieve the expectations in
mathematics and is an integral part of the Ontario
mathematics curriculum.

9. Advantages of problem solving
• increases opportunities for the use of critical
thinking skills (e.g., selecting appropriate tools
and strategies, estimating, evaluating, classifying,
assuming, recognizing relationships, conjecturing,
posing questions, offering opinions with reasons,
making judgments) to develop mathematical
reasoning;
• helps all students develop a positive math
identity;
• allows all students to use the rich prior
mathematical knowledge they bring to school;

10. Mathematical Processes
• helps all students make connections among
mathematical knowledge, concepts, and skills,
and between the classroom and situations
outside the classroom;
• promotes the collaborative sharing of ideas and
strategies and promotes talking about
mathematics;
• facilitates the use of creative-thinking skills when
developing solutions and approaches;
• helps students find enjoyment in mathematics
and become more confident in their ability to do
mathematics.

11. Reasoning and Proving
• Reasoning and proving are a mainstay of mathematics
and involves students using their understanding of
mathematical knowledge, concepts, and skills to justify
their thinking.
• Proportional reasoning, algebraic reasoning, spatial
reasoning, statistical reasoning, and probabilistic
reasoning are all forms of mathematical reasoning.
Students also use their understanding of numbers and
operations, geometric properties, and measurement
relationships to reason through solutions to problems.

12. Strategies of reasoning
• Teachers can provide all students with learning
opportunities where they must form
mathematical conjectures and then test or prove
them to see if they hold true.
• Initially, students may rely on the viewpoints of
others to justify a choice or an approach to a
solution. As they develop their own reasoning
skills, they will begin to justify or prove their
solutions by providing evidence.

13. Mathematical Processes
Reflecting
• Students reflect when they are working through a
problem to monitor their thought process, to
identify what is working and what is not working,
and to consider whether their approach is
appropriate or whether there may be a better
approach.
• Students also reflect after they have solved a
problem by considering the reasonableness of
their answer and whether adjustments need to
be made.

14. Strategies of reflecting
• Teachers can support all students as they develop
their reflecting and met cognitive skills by asking
questions that have them examine their thought
processes, as well as questions that have them
think about other students’ thought processes.
• Students can also reflect on how their new
knowledge can be applied to past and future
problems in mathematics.

15. Mathematical Processes
Connecting
• Experiences that allow all students to make
connections – to see, for example, how knowledge,
concepts, and skills from one strand of mathematics
are related to those from another – will help them to
grasp general mathematical principles.
• Through making connections, students learn that
mathematics is more than a series of isolated skills and
concepts and that they can use their learning in one
area of mathematics to understand another.
• Seeing the relationships among procedures and
concepts also helps develop mathematical
understanding.

16. Mathematical Processes
Strategies of connecting
• making connections between the mathematics
they learn at school and its applications in their
everyday lives not only helps students
understand mathematics but also allows them to
understand how useful and relevant it is in the
world beyond the classroom.
• These kinds of connections will also contribute to
building students’ mathematical identities.

17. Mathematical Processes
Communicating
• Communication is an essential process in learning
mathematics. Students communicate for various
purposes and for different audiences, such as the
teacher, a peer, a group of students, the whole
class, a community member, or their family.
• They may use oral, visual, written, or gestural
communication. Communication also involves
active and respectful listening.
• Teachers provide differentiated opportunities for
all students to acquire the language of
mathematics,

18. Advantages of communicating
• share and clarify their ideas, understandings,
and solutions;
• create and defend mathematical arguments;
• provide meaningful descriptive feedback to
peers; and
• pose and ask relevant questions.

19. Representing
• Students represent mathematical ideas and
relationships and model situations using tools,
pictures, diagrams, graphs, tables, numbers,
words, and symbols.
• Teachers recognize and value the varied
representations students begin learning with, as
each student may have different prior access to
and experiences with mathematics.
• While encouraging student engagement and
affirming the validity of their representations,

20. Strategies of representing
• teachers help students reflect on the appropriateness
of their representations and refine them.
• Teachers support students as they make connections
among various representations that are relevant to
both the student and the audience they are
communicating with, so that all students can develop a
deeper understanding of mathematical concepts and
relationships.
• All students are supported as they use the different
representations appropriately and as needed to model
situations, solve problems, and communicate their
thinking.

21. Mathematical Processes
Selecting Tools and Strategies to
improve mathematical processes
• Technology. A wide range of technological and
digital tools can be used in many contexts for
students to interact with, learn, and do
mathematics.

22. Mathematical Processes
• see patterns and relationships;
• make connections between mathematical
concepts and between concrete and abstract
representations;
• test, revise, and confirm their reasoning;
• remember how they solved a problem;
• communicate their reasoning to others,
including by gesturing.

23. Mathematical Processes
• dynamic geometry software and online geometry
tools to develop spatial sense;
• computer programs to represent and simulate
mathematical situations (i.e., mathematical
modeling);
• communications technologies to support and
communicate their thinking and learning;
• computers, tablets, and mobile devices to access
mathematical information available on the
websites of organizations around the world and
to develop information literacy.

24. Mathematical Processes
• Tools. All students should be encouraged to
select and use tools to illustrate mathematical
ideas. Students come to understand that
making their own representations is a
powerful means of building understanding
and of explaining their thinking to others.
Using tools helps students

25. Mathematical Processes
• Strategies and Conclusion
• Problem solving often requires students to select
an appropriate strategy. Students learn to judge
when an exact answer is needed and when
an estimate is all that is required, and they use
this knowledge to guide their selection.
• For example, computational strategies include
mental computation and estimation to develop a
sense of the numbers and operations involved.

26. Mathematical Processes
• . The selection of a computational strategy is
based on the flexibility students have with
applying operations to the numbers they are
working with.
• Sometimes, their strategy may involve the use
of algorithmsthe composition and decomposit
ion of numbers using known facts. Students
can also create computational representations
of mathematical situations using code.